Continuous and Discrete Fourier Transforms, Extension Problems and Wiener-Hopf Equations

Inhaltsverzeichnis

• Uncertainty principles for time-frequency operators.
• 1. Introduction.
• 2. Sampling results for time-frequency transformations.
• 3. Uncertainty principles for exact Gabor and wavelet frames.
• References.
• Distribution of zeros of matrix-valued continuous analogues of orthogonal polynomials.
• 1. Preliminary results.
• 2. Orthogonal operator-valued polynomials.
• 3. Zeros of mat rix-valued Krein functions.
• The band extension of the real line as a limit of discrete band extensions, II. The entropy principle.
• 0. Introduction.
• I. Preliminaries.
• II. Main results.
• Weakly positive matrix measures, generalized Toeplitz forms, and their applications to Hankel and Hilbert transform operators.
• 1. Lifting properties of generalized Toeplitz forms and weakly positive matrix measures.
• 2. The GBT and the theorems of Helson-Szegö and Nehari.
• 3. GNS construction, Wold decomposition and abstract lifting theorems.
• 4. Multiparameter and n-conditional lifting theorems, the A-A-K theorem and applications in several variables.
• Reduction of the abstract four block problem to a Nehari problem.
• 1. Main theorems.
• 2. Proofs of the main theorems.
• The state space method for integro-differential equations of Wiener-Hopf type with rational matrix symbols.
• 1. Introduction and main theorems.
• 2. Preliminaries on matrix pencils.
• 3. Singular differential equations on the full-line.
• 4. Singular differential equations on the half-line.
• 5. Preliminaries on realizations.
• 6. Proof of theorem 1.1.
• 7. Proofs of theorems 1.2 and 1.3.
• 8. An example.
• Symbols and asymptotic expansions.
• I. Smooth symbols on Rn.
• II. Piecewise smooth symbols on T.
• III. Piecewise smooth symbols on Rn.
• IV. Symbolsdiscontinuous across a hyperplane in Rn × Rn.
• Program of Workshop.